Question 9 Is this a legal application of a certain rule? If so which rule? Mv (C v Z) Mv~(~Co~Z) Assoc Dist Add Conj DM Simp DS O O 0 000 0

Q: Task 1 Consider the following subset of R?: S:= {(r, sin(1/z)); z€ (0, 1/a]}. Show that 3 = S' = as…

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Q: • Show that cos z is surjective: i.e., for any w E C, there exists z E C s.t. cos z = w. (Hint: You…

A: Like in real field, a complex-valued function also exhibits injective and surjective properties.…

Q: sec? a tan zdz Evaluate +C

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Q: D Question 2 Select all that apply: r y" + 3ry - 2y = In r 3rd order O linear Ononlinear O 2nd order…

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Q: Given f(x, y) = sin(x + y) where x = s*t°, y = 3s – 2t. Find f.(x(s, t), y(s, t)) = f:(æ(s, t), y(s,…

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Q: Consider the following ODE y' = y+t/y+1 Which kind of ODE is ?

A: Given ODE is y'=y+ty+1. Simplify y'=y+ty+1. ⇒dydt=y+ty+1⇒y+1dydt=y+t⇒y+1dydt−y=t..........1 Since,…

Q: _4. Arg (zz) = 0, whenever :+0. _5. Arg(=)= arctan 2| for x +0, wherex= Re(z) and y = Im (z). 6. Arg…

A: This is a problem of complex analysis.

Q: 13 Given: LA = LE, AB = BE, FB 1 AE, 22 = 23 F 23 4. В Prove: CB = DB A E

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Q: Given f(x, y) = sin(x + y) where a s*t°, y = 2s – 6t. Find f.(x(s, t), y(s, t)) = fi(#(s, t), y(s,…

A: we have calculate the f_s( x(s,t) ,y(s,t)  and f_s( x(s,t) ,y(s,t)

Q: Find a value of c so that P(Z <c)= 0.65. a) O 0.39 b) O 0.89 c) O-0.39 d) O 0.61 e) O 1.39 f) O None…

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Q: つ1 BC. T (o,f)= 1 , T(h,f) = (os f. エ、(.T(メ,o)= ズ.

A: According to the given information, it is required to solve the heat equation.

Q: Q6. Let w = f(r,0), r = √x' + y³, 0 = tan'(y/x), ), find aw ?х > and ди ду in terms of r and 0.

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Q: What are the values of e and cz so that y(x) = c, sin(x) + czcos(x) will satisfy the conditions y(0)…

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Q: Let a b. A = d Lg h i Find a. det(3A) b. det ((2A¬)) P Type here to search %23

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Q: Let r(t) = (et, t2 + 1, h(t)). If |r' (0)| = √2, which of the following is a possible h(t)? O sin(t)…

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Q: (6, OsI<A ). y' +9y = g(t), y(0)=1, y'(0)=3, where g(t)= 0, ISI<00

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Q: Find the following:

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Q: The ODE M(z. v) dz + N(z. v) du = 0 is exact if and only if

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Q: Let o e C (RN), heRN - {0}. For te IR', we set (x + th) – (x) (x) = 1- Show that E C (IRN).

A: Since, you have post multiple question. I am answering first one. Please post again for the rest…

Q: QUESTION 6 Consider the function f(r, y, z) = 6x² + 4xy+ e4yz af Then is equal to: ду O A. 4x +…

A: we find out partial derivative with respect to y.   see 2nd step.

Q: If V=p°z°sino., compute the magnitude of E(1,0°, 1), (Here (1,0", 1) is in eylindrical coordinates…

A: In this question, we have to find the magnitude of the vector E at a given point.

Q: Let w = a*y cos(4z). Find the following. (a) (x, Y, 2) = (b) (x, Y, z) = ду (c) (x, Y, z) az (d) (2,…

A: In this question we will use basic of calculus i.e concept of partial differentiation. We will…

Q: calculate d cos(u) for following choices of U(x) d u«)=10-x, ax Cos(UCx) = uc^)= x? corfuca) ulx) =…

A: The general rule for the derivative ddxcos(u(x)) is the following. By the chain rule,…

Q: Let X1,..., Xn be i.i.d. Gamma(a, B) with a > 0 and B > 0. Find the MMES of a and В.

A: Let x1, ..., xn be the i.i.d Gamma(α, β) ;α&gt;0, β&gt;0. Find the Method of Moment Estimator of α…

Q: Question 6. Let u := Vr+ 82, with r:=y+x cost and s := x+y sin t, with t, x, y € R. [6] Determine if…

A: Here we use basic rule of chain rule

Q: Quèstion 14 2я 2 2 Compute Srll dz dr de 0 07 215 % O A. 168 214 ОВ. 168 212 O C. 168 21 O D. 168 O…

A: Solve as integration

Q: Consider the following figure. D F OC = 8 and OE = 4 OE I CD in 00 Given: %3D Find: CD CD =

A: Answer

Q: S 1.Prove that L (coswt): %| s2 +w2

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Q: Suppose E, F C S with Pr[E] = 0.2, Pr[F] = 0.5 and Pr[E' n F] = 0.45. What is Pr[E\F]? %3D %3D

A: We have, E, Fc S with Pr[E] = 0.2, Pr[F] = 0.5 and Pr[E' ∩ F)=0.45. We want to find, Pr(E|F)

Q: For what value of Ⓒ is cotⒸ undefined? 1.0⁰ II. 180° III. 270⁰ Olonly OI and III only OI and II only…

A: This question is related to trigonometric ratios, we will solve it using given information.

Q: Consider the following formula: A By(F(x) → F(y)) Both 3xA and VxA are theorems. VxA is a theorem,…

A: This question is about application theorem formulation

Q: en Gx) show that GCxx) = to is a t Slution to x y" + Cy')a = c

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Q: m!n! If m, n e N, then prove that ,, dx = m.n (m+n+1)!

A: A detailed solution is given below.

Q: • Show that cos z is surjective: i.e., for any w E C, there exists z E C s.t. cos z = w. (Hint: You…

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Q: (10) Without finding T and N, write a(t) in the forma(t) = a-T + ayÑ at t= r(t) =

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Q: 2丁 o<ズくL メ BC. TlU,A)=0, TIL,f)=COSf エ、C. T(メ、0)=o

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Q: Question 1: Let y(r, t) = x'tº + 2x – 3t (a) What is du/az? (b) What is du/a?

A: We have , yx , t = x7 t9 + 2x - 3t We need to find , ∂y∂x and ∂y∂t. We know that , partial…

Q: QUESTION 7. Given that F(x, y, z)=sin x i+cos yj+xz k. Evaluate , F.dr where C is given by…

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Q: MAC 2313: 15.2 Worksheet 1. Evaluate ffr cos ydA, R is bounded by y = 0, y = a?, a = 1.

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Q: az az and du #6. Use the Chain Rule to determine given that av z = x sin (y? – x) x = 3u – v?, y =…

A: Solution:-

Q: -EB = DC %3D AE=AD; Example 3: Given: Prove: B=C E, B C.

A: We will use the congruency method to find solution to the problem .

Q: QUESTION 5 Complete the proof using the drop-down menu. Prove: (A xB)N(C×D)c(ANC)x(B ND). VE(AXB)N(C…

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Q: If z=1+y , I= e' cos(s) and y=e' sin(s), then at (t, s) = (1,0) is as O-2e O 2e O 2e

A: if z=x2+y2 where x=et coss , y=et sins then find ∂z∂s at t,s=1,0

Q: 1 1 The identity I = [ |" dixcy=f, S* * dydx is

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Q: et A E C. Show that |A| 1 if and only if A= e for some 0 E R. %3D

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Q: Given f(x, y) = sin(x + y) where x = = s*t*, y = 3s – 4t. Find - f.(x(s, t), y(s, t)) = fi(x(s, t),…

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Q: Find C if r(t) = ⟨et, 3 cos t, t + 10⟩ + C and r(0) = ⟨0, 0, 0⟩.

A: We have given function r(t)   r(t) = ⟨et, 3 cos t, t+10⟩ +C   We have to find the value of C   It…

Q: 2. If f (x) = * +2 and g (z) = - and h (z) = 2I + 1 find the following |3D fog= b. hof= c. hog= d.…

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Q: Which of the following is equal to S ešin ® de ? A. e+ cos e+ C 8. ecos + C Option 1 Option 2 C.…

A: Given:    Intergral of esinθ dθ

Q: Let w = r. In(xyz), then which of the following is 2 O a. O b.0 O d. O e.

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